{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analyze Big Financial Data**\n",
    "\n",
    "O'Reilly (2014)\n",
    "\n",
    "Yves Hilpisch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img style=\"border:0px solid grey;\" src=\"http://hilpisch.com/python_for_finance.png\" alt=\"Python for Finance\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Buy the book ** |\n",
    "<a href='http://shop.oreilly.com/product/0636920032441.do' target='_blank'>O'Reilly</a> |\n",
    "<a href='http://www.amazon.com/Yves-Hilpisch/e/B00JCYHHJM' target='_blank'>Amazon</a>\n",
    "\n",
    "**All book codes & IPYNBs** |\n",
    "<a href=\"http://oreilly.quant-platform.com\">http://oreilly.quant-platform.com</a>\n",
    "\n",
    "**The Python Quants GmbH** | <a href='http://tpq.io' target='_blank'>http://tpq.io</a>\n",
    "\n",
    "**Contact us** | <a href='mailto:pff@tpq.io'>pff@tpq.io</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introductory Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import plt\n",
    "plt.style.use('seaborn')\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "import warnings; warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implied Volatilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "uuid": "8e3ac03d-e5c1-4184-8494-5c02f5c1a897"
   },
   "outputs": [],
   "source": [
    "V0 = 17.6639"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "uuid": "3d727b16-4ff1-49fb-a54a-6e96568f54b0"
   },
   "outputs": [],
   "source": [
    "r = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "uuid": "009042d8-f384-482c-8b4b-eeac6312315e"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "h5 = pd.HDFStore('./source/vstoxx_data_31032014.h5', 'r')\n",
    "futures_data = h5['futures_data']  # VSTOXX futures data\n",
    "options_data = h5['options_data']  # VSTOXX call option data\n",
    "h5.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import datetime as dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "futures_data['DATE'] = futures_data['DATE'].apply(lambda x: dt.datetime.fromtimestamp(x / 1e9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "futures_data['MATURITY'] = futures_data['MATURITY'].apply(lambda x: dt.datetime.fromtimestamp(x / 1e9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "uuid": "8d5c855d-87d0-4108-93c7-57094610bd68"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DATE</th>\n",
       "      <th>EXP_YEAR</th>\n",
       "      <th>EXP_MONTH</th>\n",
       "      <th>PRICE</th>\n",
       "      <th>MATURITY</th>\n",
       "      <th>TTM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>4</td>\n",
       "      <td>17.85</td>\n",
       "      <td>2014-04-18 02:00:00</td>\n",
       "      <td>0.049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>5</td>\n",
       "      <td>19.55</td>\n",
       "      <td>2014-05-16 02:00:00</td>\n",
       "      <td>0.126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>6</td>\n",
       "      <td>19.95</td>\n",
       "      <td>2014-06-20 02:00:00</td>\n",
       "      <td>0.222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>7</td>\n",
       "      <td>20.40</td>\n",
       "      <td>2014-07-18 02:00:00</td>\n",
       "      <td>0.299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>8</td>\n",
       "      <td>20.70</td>\n",
       "      <td>2014-08-15 02:00:00</td>\n",
       "      <td>0.375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>9</td>\n",
       "      <td>20.95</td>\n",
       "      <td>2014-09-19 02:00:00</td>\n",
       "      <td>0.471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>10</td>\n",
       "      <td>21.05</td>\n",
       "      <td>2014-10-17 02:00:00</td>\n",
       "      <td>0.548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014</td>\n",
       "      <td>11</td>\n",
       "      <td>21.25</td>\n",
       "      <td>2014-11-21 01:00:00</td>\n",
       "      <td>0.644</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   DATE  EXP_YEAR  EXP_MONTH  PRICE            MATURITY    TTM\n",
       "496 2014-03-31 02:00:00      2014          4  17.85 2014-04-18 02:00:00  0.049\n",
       "497 2014-03-31 02:00:00      2014          5  19.55 2014-05-16 02:00:00  0.126\n",
       "498 2014-03-31 02:00:00      2014          6  19.95 2014-06-20 02:00:00  0.222\n",
       "499 2014-03-31 02:00:00      2014          7  20.40 2014-07-18 02:00:00  0.299\n",
       "500 2014-03-31 02:00:00      2014          8  20.70 2014-08-15 02:00:00  0.375\n",
       "501 2014-03-31 02:00:00      2014          9  20.95 2014-09-19 02:00:00  0.471\n",
       "502 2014-03-31 02:00:00      2014         10  21.05 2014-10-17 02:00:00  0.548\n",
       "503 2014-03-31 02:00:00      2014         11  21.25 2014-11-21 01:00:00  0.644"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "futures_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "options_data['DATE'] = options_data['DATE'].apply(lambda x: dt.datetime.fromtimestamp(x / 1e9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "options_data['MATURITY'] = options_data['MATURITY'].apply(lambda x: dt.datetime.fromtimestamp(x / 1e9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "uuid": "48b29f70-8142-4960-8d4d-3a241685bc1d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 395 entries, 46170 to 46564\n",
      "Data columns (total 8 columns):\n",
      "DATE         395 non-null datetime64[ns]\n",
      "EXP_YEAR     395 non-null int64\n",
      "EXP_MONTH    395 non-null int64\n",
      "TYPE         395 non-null object\n",
      "STRIKE       395 non-null float64\n",
      "PRICE        395 non-null float64\n",
      "MATURITY     395 non-null datetime64[ns]\n",
      "TTM          395 non-null float64\n",
      "dtypes: datetime64[ns](2), float64(3), int64(2), object(1)\n",
      "memory usage: 27.8+ KB\n"
     ]
    }
   ],
   "source": [
    "options_data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "dead6085-55a7-46c1-9396-3ec0e247b8f4"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DATE</th>\n",
       "      <th>MATURITY</th>\n",
       "      <th>TTM</th>\n",
       "      <th>STRIKE</th>\n",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>46170</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014-04-18 02:00:00</td>\n",
       "      <td>0.049</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46171</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014-04-18 02:00:00</td>\n",
       "      <td>0.049</td>\n",
       "      <td>2.0</td>\n",
       "      <td>15.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46172</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014-04-18 02:00:00</td>\n",
       "      <td>0.049</td>\n",
       "      <td>3.0</td>\n",
       "      <td>14.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46173</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014-04-18 02:00:00</td>\n",
       "      <td>0.049</td>\n",
       "      <td>4.0</td>\n",
       "      <td>13.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46174</th>\n",
       "      <td>2014-03-31 02:00:00</td>\n",
       "      <td>2014-04-18 02:00:00</td>\n",
       "      <td>0.049</td>\n",
       "      <td>5.0</td>\n",
       "      <td>12.85</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     DATE            MATURITY    TTM  STRIKE  PRICE\n",
       "46170 2014-03-31 02:00:00 2014-04-18 02:00:00  0.049     1.0  16.85\n",
       "46171 2014-03-31 02:00:00 2014-04-18 02:00:00  0.049     2.0  15.85\n",
       "46172 2014-03-31 02:00:00 2014-04-18 02:00:00  0.049     3.0  14.85\n",
       "46173 2014-03-31 02:00:00 2014-04-18 02:00:00  0.049     4.0  13.85\n",
       "46174 2014-03-31 02:00:00 2014-04-18 02:00:00  0.049     5.0  12.85"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "options_data[['DATE', 'MATURITY', 'TTM', 'STRIKE', 'PRICE']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "808a0269-42d5-43ed-b753-28abb46820de"
   },
   "outputs": [],
   "source": [
    "options_data['IMP_VOL'] = 0.0\n",
    "  # new column for implied volatilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "233c9f45-d3c4-48f4-8422-7e77c490d232"
   },
   "outputs": [],
   "source": [
    "from bsm_functions import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "uuid": "8da4e671-cbbc-44fd-8050-c8fe300a4501"
   },
   "outputs": [],
   "source": [
    "tol = 0.5  # tolerance level for moneyness\n",
    "for option in options_data.index:\n",
    "    # iterating over all option quotes\n",
    "    forward = futures_data[futures_data['MATURITY'] == \\\n",
    "                options_data.loc[option]['MATURITY']]['PRICE'].values[0]\n",
    "      # picking the right futures value\n",
    "    if (forward * (1 - tol) < options_data.loc[option]['STRIKE']\n",
    "                             < forward * (1 + tol)):\n",
    "        # only for options with moneyness within tolerance\n",
    "        imp_vol = bsm_call_imp_vol(\n",
    "                V0,  # VSTOXX value \n",
    "                options_data.loc[option]['STRIKE'],\n",
    "                options_data.loc[option]['TTM'],\n",
    "                r,   # short rate\n",
    "                options_data.loc[option]['PRICE'],\n",
    "                sigma_est=2.,  # estimate for implied volatility\n",
    "                it=100)\n",
    "        options_data.ix[option, 'IMP_VOL'] = imp_vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "94491814-c0c6-4565-b1f7-cedb1af12c48"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "496   2014-04-18 02:00:00\n",
       "497   2014-05-16 02:00:00\n",
       "498   2014-06-20 02:00:00\n",
       "499   2014-07-18 02:00:00\n",
       "500   2014-08-15 02:00:00\n",
       "501   2014-09-19 02:00:00\n",
       "502   2014-10-17 02:00:00\n",
       "503   2014-11-21 01:00:00\n",
       "Name: MATURITY, dtype: datetime64[ns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "futures_data['MATURITY']\n",
    "  # select the column with name MATURITY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "cbb44f1e-2ab5-4d8f-976a-2d36515eef12"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DATE         2014-03-31 02:00:00\n",
       "EXP_YEAR                    2014\n",
       "EXP_MONTH                      4\n",
       "TYPE                           C\n",
       "STRIKE                         1\n",
       "PRICE                      16.85\n",
       "MATURITY     2014-04-18 02:00:00\n",
       "TTM                        0.049\n",
       "IMP_VOL                        0\n",
       "Name: 46170, dtype: object"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "options_data.loc[46170]\n",
    "  # select data row for index 46170"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "uuid": "e267720a-901b-42fd-86eb-f31c29ebc166"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "options_data.loc[46170]['STRIKE']\n",
    "  # select only the value in column STRIKE\n",
    "  # for index 46170 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "03092953-5496-4500-9cf5-e3cbcf46d396"
   },
   "outputs": [],
   "source": [
    "plot_data = options_data[options_data['IMP_VOL'] > 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "738b9618-b3a9-434f-a685-441a0c837b76"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Timestamp('2014-04-18 02:00:00'),\n",
       " Timestamp('2014-05-16 02:00:00'),\n",
       " Timestamp('2014-06-20 02:00:00'),\n",
       " Timestamp('2014-07-18 02:00:00'),\n",
       " Timestamp('2014-08-15 02:00:00'),\n",
       " Timestamp('2014-09-19 02:00:00'),\n",
       " Timestamp('2014-10-17 02:00:00'),\n",
       " Timestamp('2014-11-21 01:00:00')]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maturities = sorted(set(options_data['MATURITY']))\n",
    "maturities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "8886807a-ca71-48d0-b5ef-ab7cb9470548"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cdtss3NzcOHHiGIMGDcXZ2dnmbHJ5ebkMHRpDWFgYZWVlrFjxs9W5AhfLlh5m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\nGUgEeEEQBEGYgUSAFwRBEIQZ6P8DEs4bCmh6TVYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(8, 6))\n",
    "for maturity in maturities:\n",
    "    data = plot_data[options_data.MATURITY == maturity]\n",
    "      # select data for this maturity\n",
    "    plt.plot(data['STRIKE'], data['IMP_VOL'],\n",
    "             label=maturity.date(), lw=1.5)\n",
    "    plt.plot(data['STRIKE'], data['IMP_VOL'], 'r.', label='')\n",
    "plt.grid(True) \n",
    "plt.xlabel('strike')\n",
    "plt.ylabel('implied volatility of volatility')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "# tag: vs_imp_vol\n",
    "# title: Implied volatilities (of volatility) for European call options on the VSTOXX on 31. March 2014"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "uuid": "34582055-b4b2-49ea-8678-e44288f7de88"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.groupby.DataFrameGroupBy object at 0x11bbbfc88>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keep = ['PRICE', 'IMP_VOL']\n",
    "group_data = plot_data.groupby(['MATURITY', 'STRIKE'])[keep]\n",
    "group_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "uuid": "1b5253de-0b31-4af0-8155-b2c405363a0d"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>PRICE</th>\n",
       "      <th>IMP_VOL</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MATURITY</th>\n",
       "      <th>STRIKE</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">2014-04-18 02:00:00</th>\n",
       "      <th>9.0</th>\n",
       "      <td>8.85</td>\n",
       "      <td>2.083388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.0</th>\n",
       "      <td>7.85</td>\n",
       "      <td>1.804193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11.0</th>\n",
       "      <td>6.85</td>\n",
       "      <td>1.550283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12.0</th>\n",
       "      <td>5.85</td>\n",
       "      <td>1.316103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13.0</th>\n",
       "      <td>4.85</td>\n",
       "      <td>1.097184</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            PRICE   IMP_VOL\n",
       "MATURITY            STRIKE                 \n",
       "2014-04-18 02:00:00 9.0      8.85  2.083388\n",
       "                    10.0     7.85  1.804193\n",
       "                    11.0     6.85  1.550283\n",
       "                    12.0     5.85  1.316103\n",
       "                    13.0     4.85  1.097184"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_data = group_data.sum()\n",
    "group_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "390e4908-23ed-4419-a62d-b25ed3cf2d15"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FrozenList([[2014-04-18 02:00:00, 2014-05-16 02:00:00, 2014-06-20 02:00:00, 2014-07-18 02:00:00, 2014-08-15 02:00:00, 2014-09-19 02:00:00, 2014-10-17 02:00:00, 2014-11-21 01:00:00], [9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0, 26.0, 27.0, 28.0, 29.0, 30.0]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_data.index.levels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "13a3c945-2ae9-4583-b21f-cb6d4e4729b8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.021352235143176"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from bsm_functions import bsm_call_value\n",
    "S0 = 100.\n",
    "K = 105.\n",
    "T = 1.0\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "bsm_call_value(S0, K, T, r, sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "aebfedcc-472c-4225-82eb-6405ecf7eaa9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "European Option Value   7.999\n",
      "Duration in Seconds    16.315\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run mcs_pure_python.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "d038ec31-373b-4979-aa49-a47ff96fc234"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.999"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_val = 0.0\n",
    "for path in S:\n",
    "    # C-like iteration for comparison\n",
    "    sum_val += max(path[-1] - K, 0)\n",
    "C0 = exp(-r * T) * sum_val / I\n",
    "round(C0, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vectorization with NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "uuid": "2f695395-b7b7-4d0c-bab3-659fcd4da5d0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "v = list(range(1, 6))\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "548c6e07-9435-421c-9408-d63252608f74"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "uuid": "0a831df5-d2c3-46af-8399-ad2b4b411001"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "v = np.arange(1, 6)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "4c5153ff-983f-4ee1-95d6-0dae809da4bf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  4,  6,  8, 10])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "0fca4476-2003-4733-a6e1-f405997e1b1a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "European Option Value   8.020\n",
      "Duration in Seconds     1.147\n"
     ]
    }
   ],
   "source": [
    "%run mcs_vector_numpy.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "6d10a22b-fed3-4627-a2bc-6f958824ca2f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.22"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(tpy / tnp1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Full Vectorization with Log Euler Scheme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "uuid": "02a121e5-75ff-4ad1-9812-ec0e69d3ebaa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "European Option Value   8.023\n",
      "Duration in Seconds     1.710\n"
     ]
    }
   ],
   "source": [
    "%run mcs_full_vector_numpy.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graphical Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "f880bd6e-72fa-4906-b2a7-24f3c7419338"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'index level')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6TfsVydkexqTVoL8KA9qASixJ0tNDXRBBEAbOs28PMb+PpAUL+7WsRE80CQlk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\npRppUFBKKdVIg4JSSqlGGhSUUko1+n/mZIXXSrT3dQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(S[:, :10])\n",
    "plt.grid(True)\n",
    "plt.xlabel('time step')\n",
    "plt.ylabel('index level')\n",
    "# tag: index_paths\n",
    "# title: The first 10 simulated index level paths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "997e2c48-f4e4-49c2-be9b-ce2ed0a2166f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'frequency')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.grid(True)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "# tag: index_histo\n",
    "# title: Histogram of all simulated end of period index level values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "uuid": "bc4f9174-c92c-4abf-9d31-da3e7d0baec5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 50000)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ur0WZeW/Z10Lg1Ii4HZjGoz2js4HlEXECsDtwZIfHLUmqbKxAiYg4Arg5Iobf4XXAaBtm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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.maximum(S[-1] - K, 0), bins=50)\n",
    "plt.grid(True)\n",
    "plt.xlabel('option inner value')\n",
    "plt.ylabel('frequency')\n",
    "plt.ylim(0, 50000)\n",
    "# tag: option_iv_hist\n",
    "# title: Histogram of all simulated end of period option inner values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "d5aed456-001a-423c-9366-df294f1c3f0b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "268632"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(S[-1] < K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Technical Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "uuid": "dcba1a61-94e3-47dd-ab54-2c688e740741"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "3b6ce702-6a8c-400c-a6fc-d382f316dd9c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 1972 entries, 2010-01-04 to 2017-10-31\n",
      "Data columns (total 1 columns):\n",
      "Close    1972 non-null float64\n",
      "dtypes: float64(1)\n",
      "memory usage: 30.8 KB\n"
     ]
    }
   ],
   "source": [
    "raw = pd.read_csv('source/tr_eikon_eod_data.csv',\n",
    "                   index_col=0, parse_dates=True)\n",
    "AAPL = pd.DataFrame(raw['AAPL.O'])\n",
    "AAPL.columns = ['Close']\n",
    "AAPL.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "444a17d9-8fd1-436d-825a-3001cb080b7c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a392ef860>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H+zy7TAXTZY5PhzPbXPRfn/7aWuvngcZuh88HPjTPfwLMVkplA58G1mmt3T/N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\nQKw9lamRZ+EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "AAPL['Close'].plot(grid=True, figsize=(8, 5))\n",
    "# tag: AAPL\n",
    "# title: Historical levels of the S&P 500 index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "d134fa6d-4db4-40f3-b1ce-952ef2346e18"
   },
   "outputs": [],
   "source": [
    "AAPL['42d'] = np.round(AAPL['Close'].rolling(window=42).mean(), 2)\n",
    "AAPL['252d'] = np.round(AAPL['Close'].rolling(window=252).mean(), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "uuid": "8af03824-0abb-4747-9f8f-d517d48bd673"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Close</th>\n",
       "      <th>42d</th>\n",
       "      <th>252d</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2017-10-25</th>\n",
       "      <td>156.41</td>\n",
       "      <td>157.61</td>\n",
       "      <td>139.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-26</th>\n",
       "      <td>157.41</td>\n",
       "      <td>157.51</td>\n",
       "      <td>140.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-27</th>\n",
       "      <td>163.05</td>\n",
       "      <td>157.52</td>\n",
       "      <td>140.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-30</th>\n",
       "      <td>166.72</td>\n",
       "      <td>157.60</td>\n",
       "      <td>140.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-31</th>\n",
       "      <td>169.04</td>\n",
       "      <td>157.72</td>\n",
       "      <td>140.65</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Close     42d    252d\n",
       "Date                              \n",
       "2017-10-25  156.41  157.61  139.86\n",
       "2017-10-26  157.41  157.51  140.03\n",
       "2017-10-27  163.05  157.52  140.22\n",
       "2017-10-30  166.72  157.60  140.43\n",
       "2017-10-31  169.04  157.72  140.65"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAPL[['Close', '42d', '252d']].tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "uuid": "4dc6ac7e-6fac-4994-811b-35789c551de7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a3939a710>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NwDmACM6CIJxU9c12vtlVBECAzt2tvaVsJwCTovq+WUVavHtMc5YpBrVahdGg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\nZlLTJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "AAPL[['Close', '42d', '252d']].plot(grid=True, figsize=(8, 5))\n",
    "# tag: AAPL_trend\n",
    "# title: The Apple, Inc. stock price with 42d and 252d trend lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "uuid": "ccc2b0e9-5ab7-49c1-8054-3a1e1b23ab92"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2017-10-25    17.75\n",
       "2017-10-26    17.48\n",
       "2017-10-27    17.30\n",
       "2017-10-30    17.17\n",
       "2017-10-31    17.07\n",
       "Name: 42-252, dtype: float64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAPL['42-252'] = AAPL['42d'] - AAPL['252d']\n",
    "AAPL['42-252'].tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "e127f7c9-8e7f-4038-b490-502e6bf436f7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2010-01-04   NaN\n",
       "2010-01-05   NaN\n",
       "2010-01-06   NaN\n",
       "2010-01-07   NaN\n",
       "2010-01-08   NaN\n",
       "Name: 42-252, dtype: float64"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAPL['42-252'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "AAPL.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "uuid": "d1125e1b-3cd0-4274-aee7-9b1136db8c02"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " 1    1260\n",
       "-1     445\n",
       " 0      16\n",
       "Name: Position, dtype: int64"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SD = 0.5\n",
    "AAPL['Position'] = np.where(AAPL['42-252'] > SD, 1, 0)\n",
    "AAPL['Position'] = np.where(AAPL['42-252'] < -SD, -1, AAPL['Position'])\n",
    "AAPL['Position'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "uuid": "ffec4dc1-ebb4-43e1-962d-1fbc465afee1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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81Uh/e3OyXI7rHbM4KGY2C/gccKe7f83M2kP+ctPxnE8H/tzMHiAZv/m2nGOV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\niLQ4FQIRkRanQiAi0uJUCEREWtx/AP1AFlQrhdybAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "AAPL['Position'].plot(lw=1.5, grid=True)\n",
    "plt.ylim([-1.1, 1.1]);\n",
    "# tag: AAPL_signal\n",
    "# title: Positions over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "uuid": "0e51676f-7b84-441d-8191-08799247774c"
   },
   "outputs": [],
   "source": [
    "AAPL['Market'] = np.log(AAPL['Close'] / AAPL['Close'].shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "uuid": "25f3c42a-ec95-46e3-a194-4e29f0c830af"
   },
   "outputs": [],
   "source": [
    "AAPL['Strategy'] = AAPL['Position'].shift(1) * AAPL['Market']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "uuid": "ce759e67-918d-432c-a411-b22c6777dac5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gNzAiY1hAf29YA74pXek9vmLixZw+6uQu3ytYGCcnGDHotTWHiwV+6L/rA86j\nJe/ITk8EwGLr2wzOIowFQehXtNktOF1OMhM1h5ufKOESAEbHXzgNSRvEI/P+5hVOADvqfeEwjhiT\ni3QXZxhzqmeetx1zEzfPuA693tChpu50BZqpdTodyYZAJ7Sp+ZMCShUm6ANDfJx0PpnF1/uWsb56\nc8zjS+u17YMLxp7FUUXTu5V9K9hMnWDSe1NV2sN8ry2WoBzTUYTxLZdM55gJBQHxx32BmKkFQehX\neDJoeeJ/J+SOIzcph9oIIUrhmOFOi+nBpDdy0rC5vL3rw5CxwaFRPYXNaQvTqgmJIWmDAE0z7ujl\nIFgzBs0jvMXuc2QLToGZlRiolXdGM15buR61voRl5Zqm++T8+6OOd7lctDus7Krfy+jMEcwfdnzM\nnxWJhhbtb+LBa2eTnGhEp9N5BWywZry/ykyj2RpQJjE1KXK8cUF2Cr88Z3K359hdRDMWBKFf4fG+\nTTQketvCCeKMhHRvjO2Vky7FpDeRk5TNXbNvI8EQ+vANt0eaYkymob0xIIVmT2FzhJqfNwRpmgad\nAReuqMLS0+ev+QaHZw1JHRRwPm/YnLD36AiL3cKiLf/xCuKO2Fyzjeu/uoWbv/kTLpeLguT4ZLBq\nadNeZDJSE7yxwQa9jgSTPkQLLqtqxgWccsxwTpyuhX0NKwgsL9kfEc1YEIR+hTVIM47E6aNOZnrB\nVGrb6hiRMYwZhdM6vPfVUy7ng92fUt6iJcg4umg6S/YvZ2/TPsZlj+n+5KMQrlzicUNmBpx7BKzD\n6UAfwenI4TVT+/qtbq17fPZYji6azjFFRwZcMyxtCCMyhnk9z10xCuPOWA3sTjv/2Ph8QFtqDIUv\nOsLcZvPGFRv9vhOdTkd2WiINQSZsc5v2PWelJTD/yCFccMJoUqJoxv0F0YwFQehXBJupI3Hc4Fmk\nmVJDnJOiMS1/EmeM/qH3vCBF09weXfdMF2baOexugfnXY//gbfMPvQKf8Hpl+5tY7OFjaz17z3qd\nTzM+pmgGg1ILuWzChcwadFTI/qxBb+B3M673fl6kfWmnyxmQFKSqtQaACTnjANBFKfSwumJdSFtG\nYnqYkZ1ja2nk7Qm9XkdTi5XFX+5iz0EtNt3s1qLTkk3odLpDQhCDCGNBEPoZPjN1qDD+zZHXkmZK\n5eopP+1yaI7Jz5mpMMVnRo2W/zoeWB12dOhIMiZGHDM0Tcuqtbryez7c81nYMcGhTQCnjpzPH2fe\nHBAmFYxOp/M6ckUqrvD53q/54/K/sblGSz/qEcYnDz+BcdnFuHBF3NN+p+QjAC4ce4637aigvfuu\n4B+iFMzBWm2f/JNVZdz54hoklYHaAAAgAElEQVQWfbjNa9JO7SAvdX9DzNSCIPQrfJqxT2jlJedS\n01ZLbnI29x1/e7fub/TTKD0aH2gZudITem5v0e6wY9QbSTYmMT1/CkpOaIIJ/ypMwTWKPXjM1F3x\nTva8wDgjhHOtqFgDwD82Ps99x93urbtckJJHkvv3aHe0k6IPND87XU5vJrR5w+YwZ8hMBhdmU10d\nPWY6HPXN7bRabAzJ136LmgatStUfLjsy2mUALN10kOEFaRj0OnLSI7/09EdEMxYEoV8RTjO+5agb\n+MPRN4Z4BXeFYI36BHdWqIYwKTjjic2pCWO9Ts/Ppyzg+CHHhozxd8Ta3bg3oEKTB68Dly40r3JH\neAR4JM14UGqR9/iWpX9hn/kAJr2JrMRM79xabKElKfeby3Hh8tZX9sR5d5ayymZufnIZf3puFe02\nB3srmvl4pZb+NC8ztAb0LZdMD71HlZlpxXmHjHnagwhjQRD6FV7N2M+cm2JK9hZG6C7Bxu2sBE3A\nh0suEk9sDluHQsrup7E2tDdyMEzRiO5oxj5hHH7PODcpO+C8qrWGoWmD0Ov05Lj7wnlWP71Bc9wq\naSzt9Jz8ueeV773HG0tqeW+ZL/NaZlrotoVHew5m5sTCbs2jLxBhLAhCv8HqsHpjgRP0PVP2zxgk\nED3JRdZUrmdPY1m4S+KCRzOOxsSccSjZxYzK0AoW+BdZ8OALber849tjbbA6w4dyhXPsGuauCuXx\n/N5RXxIyxvMCNT1/SqfnFHAfq+9l5N+fbGdflZZfetSgdG85RH9SIqSwTA5Tjam/I8JYEIQepbG9\nmT2Ne2Ma++W+pd7jtISeqSc7ImMYc4fM5tfTrwZ8CTFWV67jwbVP9MhngkcYRxcSScYkbph+NdPy\ntSQUwck7wD+0qfMCx2Od3lqrhu0PZxb35JTOSswkzZQa9gXBY7W4ZPwFnZ6TPyajnlGD0snLTKLF\nYvcm7fjjT0NrEQMBAnrRrfM549gRAIwMUy6xvyMOXIIg9Bgul4vblt0JwPVH/DzAYSqYDdWbed+v\nBOJgv/3LeKLX6fmx4ivll5XYOw9um8NGqiG2uFuP85oljOCzOjRvYWMXhLHHk/udko84pmgGmUGh\nRx5h/KOxZ/PGzvcAmF7g03bNthZv6ckttdt5asMiClMKsDvtJBkSSepibegGczu/eUKreZxoMmDW\nBSbyiOY5f/XZE70vGRecMIYLTujZePGeQoSxIAg9RqVf0oiq1poOhLGv+MO1067stSLv8YiF7YgN\n1VtotbWRl5QT03iP0NxWu4OP9nzOJeN/RHHWKAAq3PvIWVHCmCIxd8ixfLb3KwCqWqtChLFH655e\nMIVjBx1NgsEUdm/6hS2vsbZKK8bg+Y09dZW7gkcQAxiNes6aPYpFH2nhVZNGRf/OZk3smZe23qZD\nYawoih54H1gJJABjgCtVVW3zG5MEPAgcAMYC96qquqNHZiwIwiFDrV8CiaYOvJX942Yn5Y7vsTkF\nYwoqolDSUMqYrJFxuXdFSyVN1mbWuksbZgc5SEXCs7fsCTXaUrud4qxRHDAfZE/TXsZlF3eYFCUc\n/t7onlAkgJUH1zI4rcirGRt1xrDx0EfkT2Z99WZWV34f0tfZl5pWi43rH/k2pP3CecUMK0gjOyOR\nJevLuWBu10svHkrEqhl/p6rqXQCKorwLnA+84td/I1Cmqur9iqJMAZ4Dup8dXBCEQ5rqthrvcaM1\nesxpWg/G+EYjeO/1oe+f4tF5f+vQ2SoW7lz5dwCGp2sVgRZO/ElM1wWb6PVuH/BdDZp38ayiGV2a\nj7+1wZPQo7G9mX9v+y8Ak90vQZH2tgelFgVUbipMKfBqxpkJnTP3e0KW/FlwiuLNIz1pZA6TRsZm\nSTgc6NCBS1VVp58gNgJDgeDd/zOA79zjNwHTFEU59HbQBUGIK/6OW98dXB11bHaiZna9bMJFPTqn\nYMKZw+v8NPp4UNa8HwjVwiNRlFrABcVnes/b3d7Pnn3c7pjWr57yUwDaHJpz1CelX3j77O7sWoYI\nLyLBDl5D03wFKZqt5k7NIycjcH/5itPGews7DERifvVTFOUU4CbgA1VV1wR1FwD+r71N7raIdqns\n7BSMxvi6n+fn9/zeT39iIK13IK0VDo/1ulwu1lQGFnmvcB5gSmGgCdqz1uR67XFUmJPV5+tPTteT\nnxP/ORQUxK6jXJR3OoYkHYs3v4/epH1PnrCmycPHkJPctfkpCSNgE1S1V5KTm0Kp2ffCtL1+JwCD\nCrLCvqQkHQgUGfPGzsRCG1uqdnDMiGkhv1uk39HlctHoTlt51vGjOeu40QzK6xnv+d6iu3+zMQtj\nVVU/BT5VFOXfiqJcq6rqU37dVYD/TDLcbRGpr2+N1t1p8vPTu5R67VBlIK13IK0VDp/1htOUNpSp\nFOl92o//WhubtWdCS7O1z9d/sKaOdEf3TaQZCek0+ZnnO7uuqRlTWMz71DY3sGv/ARINCaSaUnGY\nDVSbu/Yd6R2aRrq+YitPf/cqZY0HAvt1empqwmu5cwuO4331f97zNrOdayf/nHJzBYUp+QHri/Z3\n/NY3u/lgeSkAI/JTMbqcff6bd4fO/JuNJLQ7NFMrijJRUZQz/Jr2AKMVRcnxM0V/CBzrHj8F2KCq\nas/mlhMEoV+z9MCKkLb3dn+Cy+WitKmMVRXfe82igLcAgb4LITvxJlzFpIb2RipaKnt1Hh4nrfXV\nm7lt2V20O6zeYhJdxb/W85L9Pi/mIndt6OwoKUdTTCne9KHgS3s5OK0ooL5yNOwOp1cQ52YkMX54\n573CD0di0YzbgZ8pijIdMAETgBuAW4E64F7gUeBBRVH+CBQDP+uZ6QqCcKiwtmoDACcNm8txQ2by\nlxUPANr+6VPrF9FibyU7M5WxyQqAnydv7wvj+4+/g99/e4f3fFfDHoakDSY32ef9/H/L7gbgpOFz\nOWnYCSFhQeGwucsmZiVmcoYyv9PzSgjjMZ2X3H2N/ZqpVwTUHj579KmcMHQO5S0Hye8gROm84jNZ\nsn85EPseuD/Pf7QdgHFDM/ndJdO7lEnscKRDYayqagma93Qwv/cb0wZcF8d5CYJwiOPxRj57zKkB\nHsuf7f2aFrtmkm6wNEEyVLfW8lGpZv6MVcOKJ6mmFKblT2aD21P4i33f8MW+b3j4hLsDNEmAL8q+\n4Yuyb3j4hLvCCkt/rA4bozKG89ujru/S9kM4j+7cOAjjyXkTuGzCRby8bTHD04dyykjtRWF05sgO\nr/XPr53chSQfeyu17+CyUxQRxH7INyEIQo/QamsjKzETo94Y4Ay0vnqT97i6pY6d9bvZVudLS9CV\nNI/x4KrJC/jl1IUBbe+6a/SG49/bFke9X01bLQ6Xgz1N3ct3fURQvud0U3wcnY4ddBSPn3gvtxx9\nQ5fv0ZWMWwa9jqQEA0MjFHkYqIgwFgShR2i1t5Ji9JW9K0opCBnz4Y4veGTd0+xp8nn0erSlFouN\nh/67nt3lHbuf7KsyU9fky+NsbrPRGqUofTh0Ol2IJvq1355qcN+6qo1R77e6Yn3U/liZmBuYtawj\nbbwzdKXyE8C5Y05nfPbYgPrLseByuahvbict+dAqb9gbiDAWBCHuOJwO2uwWUk2+XMznFZ8RcfwB\n80HvsUcz/nrdATbvqeP+V0OzPfljszu4fdEqbnn6O2/bDY9+y/WPfMP+qsixr1abg3e+3Y25zZcH\n2RBFOKUaQ/NKe1JTulwurI7ASkg57nSVXcmU5c+soqOYnDvBe95T1aw6ww9GzONX06/qtDB/6bMd\nmNts5GeF1iYe6IgwFgQh7rS5qw2l+AnjFJPvAXzisOMCxvsLY5c767/V5gz4fyQq67XMvA6ndp3N\n7hv/50WrIl731je7eW9ZKc+7cyBDeE/uj/doe9l2p520IBNxvTs5yKqK77lpyR/ZXrfT22d3aZr5\nhWPPiTr/jjDoDVwz7QqOKjwCgKykyN7O/Z3vtlQA8MOjh/XxTPofUihCEIS44nQ5vWbnVD8zdZLB\nt7+YmZCBSW/EFqZkn7sADy0WW0hfOCpqA3MWNJgDw5LMbbawZtEqtxD3CHMIb7b9YM9nNFqbabG3\nMi67mIuV89lYs4W3d33orar09X6t9OPne79mfM5YAL6v1MzYwzOGxrSOjrhswkWcNfrUuHhT9xUp\niUZSEo1MK+56UYnDFdGMBUGIK2/t/ICnN74ABOab9k/hmGhIYLBfKsVANHHsbz72aMvhKK9pCTh/\n59s9Aec3PraUcLS1ay8CKYk+nSSSmfrbA5oJvCA5l4KUPK/J2lMX2BMO5MlgBZq2n5+cy5CI6+wc\nJr3xkBbErRYb9c3tFGaLiTocIowFQYgrX+33CT9/py1/E69JbyI/OTfk2nHZxd4iCQf8hOw/3tkc\nMtaD/7j65navKdSD0+WirDI0pKipVdvjzUz17cF2tAea46665Pn/8oOrKG0qI9OvJrLnxcHmtHnr\nEguwcpu2vz5hRGyVqwYaIowFQYgb/hrs0YXTObpoethxbfa2kCo/WYmZ/Hr61Rj0BixWOweqfUJ2\njVrNjn0NPPDqOlqDzNeNLT7HqZuf9Hk//+GyI70P/jueX02juR21rN7b3+S+zmTyPQY7EsbZbqes\nQWmF3rZHvn8ah8u3T91qb+PZTS9hcbTHpfLT4cJLn2pWhKljxEQdDhHGgiDEjX3NvjzHCyddHFG4\nWZ22AG0SAtMwlh4M1WTv+8/3bNtbz7tLS7E7nGwsqcXhdLJjX2iFpeOmDmLs0Cymj/U9+G96Yhn3\n/Wcd2/dqArnFHfpkd/heIILne/yQY73HuUk5zCiYBkCy3/63C7D5eVJ/s/87byx1aTdjjA9HPCUS\nhUBEGAuCEDf8a92GI89tmk40JJIeVL84w084v/lNCQC3XDKd0YO1do/S/fmafTz34TYeeX0DV93/\nddjPGe5+4B87uSik761vAsOZHA6fVusvjH809mzOHn2q9/yvs2/1Zgfz13jTTKmU++WsrmmrDTun\ngU5uRhK5GUno9aHVoAQRxoIgxBFPesQrJ10atv/6aT/npGFzmTN4pnff1YNnT9lmd7D7QBPFQzJR\nhmdjNIQ+plZujV6wwXNNapKJ2xbMCOjbdaCR3zzhM2d7QqIg0IEr2ZhEiimZi8ady08n/DjgHv4Z\nxVJNKVS2+orUlbf4wrR+MHxe1HkOJBxOJwYRxBERYSwIQlxwupy8404fGcnrNz8ll/PHnkmCwcSY\nzJHceOzPuXbaz5iQM44zR/8Q0MzHLiAnQ3N+uuwH48LeKxr+SSWKh2Tyr9+fyI0XTvW22f204Sa/\nPWf/wgeeghUnDJ3NzEGBAt2fVGMKNodP0y7zM9V7En8I4HS6MBhEGEdCvAsEQYgLpU37vMd5YTyl\ng9HpdMwePoPq6mYm5Sredk/IUVKC9ngaWpBGSqKR1vbI6S3zs5KobtASjfzgqGFMGhX4MqDX6yI6\nDpXXtOB0utDrdQGmc0OMzldJxiTsLkfYvvROpos8nHG4v2MhPCKMBUGIC43tWg7pU0bMD0iD2Vks\nVk2wJSf6smGFE8Q/OGoYU8fkskat4pKTx1FW2UxTi5Ujxkb21p01qZAVW3wm7qPGF7BmexX7q80M\nL0wP2DM2xlg9amPNloh9R+RPjukeAwGny4VBJ8I4EiKMBUGIib1N+1hTuZ7zis8I6yVtcafAzE/p\nXuiKRzNOToj+eDprzkjSkk1eLXjMkI7TRF591iSOHJvPU+645TGDM1izvYo7nl/NolsD6w3riC44\nbjvmJv626mHveXHWKLITs/nhiHk4XU4yEtMD9pYHOg6HaMbRkD1jQRA6xOF0cP+ax/ly37ccbKnE\n5XLx8Z4vKDf7Emx4ahQndzPRRVu7phknJYYK499frMUtX332xC5X/klK8Gm8owb5PLidbkeukRnD\nAShIyY96n+DMWtmJ2Syc9BMGpxUxNH1wpysaHc40tVix2sWBKxoijAVB6JC1VRu8x+2Odr7a9y0f\n7PmUu1c95G2vbq0Buq8ZW6wezdgnNI+bogm+EUXpLLp1PrMmhoYsxYrBzzt73LAsbwYuT07r66b9\njNuOuYmCGNZx2lBfJap5w2Z3eU6HMy6Xi9uf1wp2lMRQDnOgImZqQRCi0ma38OLW17znf1/7VEC/\ny+XC7rR7iyb41zDu0ud5zNR+mvEVp4/np6cqYcOcOkuwbjZnyiA+WrGXmkYLORlaOJN/haloOBt9\njmKulizIiDJ4gGK1O2k0ax7rE0dKKsxIiDAWBCEqn+39Kmr/Y+v+SWlTmVcjTuhG/V6ny8WbS3YD\nkOTnwKXT6TDGKSwmeBs3L1OLjd6yp46c9ETyOlFr950vK0g60oCjroj/teznqrMmxmWOhwMul4tV\n2yp5+l3NwW1YQRrXnTelj2fVfxEztSAIUVlbuSFq/46GEqxOm7cmcYI+cC+3rsnClj11USsvgfbw\n/mBZKe02bc84Nalre8IdMWpQBoU5KVzqjl/2COP3l5fy+6e/i/k+JeWN4DJgWXsytj2TqW5o45HX\nN6CW1bNjXwM1jW0d3+QwZtnGcq8gBs2TPTmMH4CgId+MIAhRabW3kmhI4LSRJ3uTevx43Ln8d8c7\nIWN16AJSRTqcTn771HIAfv2jqVHr2K7cWsk7S33lD0cU9owDVILJwD1Xz/Ked0YT9ufuf691H2mq\n9q4DjQBsLPGlw3zmt/MwGQ8PnaesspnkRGNAQpVofLPOl/zk7qtmMig3Ncpo4fD4KxEEIW7srN/N\n7d/dR2VrNVaHjTa7hRHpwwLCdEz68FprVmJmwLj9Vb7KS5V1rVE/d2upr6LSbQtm9FoYTFZa183q\nQEAximDW7qiK2HeosH5nDa9/tYs7nl/N/z27osPxTpeLdpuDdWoVOuDv180RQRwDohkLghDAi1tf\no769gY/3fMHswUcBMDR9MGarT7DaXeGzYQWnwTxY57umrrk96uf67+UWxxAzHC8SjIHJPR55fQO/\n/tHUmGOEW9psmIx6bHZnmL7IWcMOBdra7Tz25kbvuX+Fq3B8u6Gc5z/e7j2fM7mI7HSp6RwLHWrG\niqKMURTlVUVRfqcoyqOKovw5zJiFiqKsUBTla/d/C3pmuoIg9DRNVq18odPlYEe95kw1LnsM0/yy\nSaWafJrO3+fe6a1N7N8OsPuAL5Rl/a6aqJ873G2WPn7qoKjj4k2wBr6xpNZbI9nlcvHw4g0s+nBb\nxOubWm0BscuTR/teSDbtPrQrOO2tCC1lGYm6JkuAIAbISO2e1WEgEYtmnAO8pqrquwCKomxVFOVD\nVVXXBo37iaqqpfGeoCAIvUdlSxUOd55lu9POtrod6HV6xmSOIsWUzN/m/JF9zQeYlDuea6ZegdVp\nI8mY6E0daQrK5/y/tfu9x1X1bZRWNDGyKHz8j8fBa8rojvNa9zRNLVay0hKpb273CtRzjhtFrtvZ\ny+lX6am51cqYIZneveICvz1V//3jQ4HSiiZe/6qEq8+eRGZqAmVVZgDOO34Ub3+7B51OM0Prw1gN\nnv8o9IVl9ODes3Ac6nQojFVVXR3UpAdawgy9XlGUCiAFeEJV1bo4zE8QhF7A6rDxv7Kv+XDP5942\ntX4XFkc7Bcl53rjbzMQMMt11hyfnTfCO9aTHdLr8qiG1+qohedi8uy6iMPaYQOMRS9xdWiyaebnU\nTzP83T+Wc8/VsyjMSfHmz/aMzc1I8p5PHp3Ll99rzkvhhFZ/5oWPtlNWZeamx5fy2K+PZ1+ltv4Z\nSgEl5U1sLKnF0u4gJSlQdLhcLra49/z/+bt5fLZ6H0X56RwxWuKKY6VTe8aKopwHfKqq6vagriXA\nh6qqViuKcjrwOnBStHtlZ6dgNMaWiD1W8vMHVvq5gbTegbRW6P31/uK9W6lvawxo8yTxyE7J6HA+\nlx5xHo989y/OmnSSd+yLL/uMZ6nJJlrabLz1zW4uPX0iHy3fw/bSeq4+b4p3fKI7lCk3J7XX15+e\nYqK51VcG0ZRoJD8/na3/2xkwTj3QxGSlkLIKn/n9zONGBbxAzJ85kmGDM/ndY98yekjgd9ff/44H\n5ad5teEbHv2W1GQTCSYDk5VCvlxfDtRi0+lC1rFysxbWVpCdzKCiTC4/a+BpxN39bWMWxoqinAic\nCNwY3Keq6h6/0y+B9xRFMaiqGr6uGFBfH92zsrPk56dTXR37/sahzkBa70BaK/T+etvsbSGC2J+C\npMIO5zM2eRyPn3gvep3eO9YjsK47bzITR+Zw3cPfALD0+308954Wf3rEuHxmFOdidzhZ/MUOAFrM\nll7/vR/51XH87D5fcpO/vbCas+eMpLwqcB4HKpuprm5mjVv4TBiRzTmzR/Dix6p3TF2tmdwUE2nu\nFxDPWg6Fv+PMlEAv+ZY2GxNHZlNXa6YoS9P+n3t3E7+56IiAcfe9tAaAVov9kFpvvOjMWiMJ7Zjs\nQYqinAGcAvwaKFIU5VhFUXIURclw99+jKIpHsI8F9kQTxIIg9B0ul4tVFd/TatOSUpQ1HQgZc4ly\ngfd43tDYci4HV3KyWO2kJZuYoRQEJHt4eLEviUhTixVzm411O2tod5t+jX0Ql6vT6bj5J0cEpGt8\nb1kp28saAsaV17ZQVtmMuU3ToudMKcKg11Neq+3cZfgJs4LsZCpqWzlYG25Xr/NYrPa43SsS4TzC\nPcU05k0fAkBDc+j2w2B36NIlPxjbg7M7vInFm3oG8F9gFvAV8C6gALcC17qHVQD/UBTlNuA2QLyp\nBaGfsqZyPS9ufY1FW14BYEONVk5wcKqv+EJRaiE/GD6PowqPoDCloEuf09xqIz0lehatlz7exk2P\nL2V7mS/GOF5pLzvLpJE5nDpzeNi+RbfOJzXJyM79Ddzx/Gpe/7oE8HkLn3TkUACuOmuS95rjpgzC\nhbZPHg8ef3MT//fsSio6iNfuDla79kI0JM/nFX/yUcMA317+/mrNjL2ttI4r7/2SO19cQ2u7jQST\nvlsFPAY6sThwrQXSOhjzaNxmJAhCj7K3eR+gOWgBrDiomRhHZY6gvEUriTgiYyhjskZ2+TMcTifm\nNhuD/R7q1503hSff3hRmrIuS/T4zuUHfdw5c0T47wWTwOnZ58GiEsyYVcqSST6LJP5+29v9Xv9jJ\nD44e1uU5NbVYufHxpd7z2iYLRTkpXb5fNDya8W9+fAT1ze0MzkshKUxd6VueXk6Du/jDnoPadkRP\nzWmg0Pdui4Ig9Boul4uv9mkPdqfLSVVrDe0O7aF60vC5AFw49pyAlJZdwexOduGvGWf6Zbr6YZBw\n8jgNeebYV0Srt1sfJmlJjtuLWqfTBQhiCI1f7iqfri4LOLe099wOoNWmCeNEk4HRgzNCBPHsyZrm\nW91gCTFpe8K+hK4hwlgQBhAezdfDX1bcD8C5Y06nMCWfJ+ffz7xhc7r3GTUt3P+f7wFIT/EJ4FS/\ncJicjCTSknumEER3CCeMZ00qDDv2T5cfFfVec9w1mPO6KaQ+XhEojFsstggjO8e2vfVcee+XvP71\nLm+bp0hHgim8aAjOpjW80Gc0NfZS+tLDFRHGgjCAqG0Lv39ZnDUqbp9x+6JVHKzV9jX9BZF/gYFE\nk57Rg8PHG/sL8N7GEGa/+mq/fWCAwpwUbl94tNexKRJ6nY7kRAM1jRZufnIZ731T0un52B2hDlXx\ncOLaWFLDA6+uAzRh/8nKMuqb2ymrbMag10WM9XY4A60Wpxzt22Mf1kOFPQYKkptaEAYIZmsLz2x6\nEYCC5Dyq2nzpKTMSoguWzuD/wD5mgs/5y/8Bb3e4wmqMt102o09zGQcn6fCfy10/n4m5zca4YVkx\n3y/BZKCt3UF9czvPvruZYyfM79R8/JOLeCiv6b4D1yOvbww4X/zVLhZ/pWnIyYmR8z+cPmsEn6z0\naeppKSaeu+VENu2uRRkmCT66g2jGgjBA2N1Y6j2+YOxZ/OFoX8qA7KT4JGnwz2W86Nb55GWGL7fX\n1m4P2WMcWZRO8dC+TRZhCNII5x0x2Hs8OC+1U4IYoNEcGgbUGTyVro6dVMSTN2l7+pt214bVmGPF\nf+974WnjQ/qjZQ1LSzZx3XlTvOeJJgM6nY6pY/JITIhvEqeBhmjGgjBA8HhPgxa6lJecw9VTLic9\nITUkRrireIpBJEV4MI8ZkkHJgSay0hJDTMI5GX3vAOS/Z3z6rBGcOXtkXO/vcrlirga1YksF/3x/\nKwApScaAWO3d5U2dfjHwsNed4vLUY4Yzd9pgVm2rDChf2ZH/3Awl33sc6XcWOo9oxoIwQPj2gFaL\n9gfD53lLHU7Ln8TozJFx+4xGs6Z1/eLsSWH7f/2jaSw8bTxzphQxImiPcdSgvt9z9BfGg3JTYhac\nkQjWMstrYzMx7682ewUx+EzH5x6n7e2X13R93/ixNzQTdZrb0/3ikwITdTg74c3el/v7hxsijAVh\nAOB0OUkyaPufZ485tUc+o67Jwtfry4FAZy1/0pJNzJ02GJ1Ox+C8VP59+yk8fuPxLDhFiZhwozfx\n9/A2xSET2J0/P4ZbLpnOcW7P6hc+jlyK0Z+DQUI72R1iNHtyEUaDjg++K+2U0PTgH440KFeLCx6S\nn8bVZ030OqTF8gLy01MVjplQEBCuJnQPMVMLwgCgqrWaFnsrM4tmxM0kHYzH/JmaZPQ+6DsiOyMJ\ne7uNE92pFvsaf1NwPKpHDcpNZVBuKrmZSSzddNAbx9sRre7wpYtPHovV5mC2J0wqK5kjx+WzalsV\ndU2WiHvykfh6nS/1qX+px1mTili1rQoIDV8Kx7wjhjDviP7xmx0uiGYsCAOAylZtL7cgJa/L9ygp\nb+S1L3ZG1Mha3Ik+LjqxuNvm3f5AvJJ2AORlJpOdnuiN443G/iozjS2a41dhdjJnHDuSzFSfBuox\nDbcGZQOLBY/z1siidIbkByZWrGu2AJDTh97sAxkRxoJwGFPVWo3F3s5ne7WKREPSBnXpPu1WB3f/\ney2frd5HeXULdoeTZ4CJe8UAACAASURBVN7bwtZSX9yyp35xaj9M5tEZPMUi/FN5xoOkBCPWDoTx\nviozf160ine+1QrhpSaFfpcmt8YeHPMbC21WTYD//MyJIX0zxmmOWZ4sW0LvImZqQThMqW6t5S8r\nHmBI2iAOmA9SkJzH5NwJXbrXS5/5SgSu2l7JB8v3ArByayWLbtViZz0FDGI1UfdXrjtvCg3m9gAz\nbjxITDDQ4HZwa7XYMBn1mIJqulf5lZY16HUUhsn37PFCD1dhqSM81ySE2Q8//dgRHDkuP0RjFnoH\nEcaCcBjS7rByx4r7ADhg1mrvzhkys0vm4x37Gli+2ZdG0yOIPWzeXcum3XWYW7V9zpQw2tyhRHJi\nYBhRvEhMMGC1ObDZnVz/yLcML0zjjiuOCRjjX4hi0qicsClDvZpxF2KNPfHJwfHUoBXJEEHcd4gw\nFnqMF1d+ztr6ldw7/7ekJPRtDGmLrZUkQyIG/cCIi9xQvTmkzeroWgKKFz7eHrX/Ib/6xABJpoHx\nHXeWpAQDDqeLfe6iGGWV5pC4493lvupVpx4T3rvcU+/Z5vCZqb/dUM6qbZVcfup48iJo9E0tVmoa\ntX3haAUxhL5B9oyFHsFis7Kq5XMcCU08uvSNPp1LTVsdv//2Dt4p+Sim8S6Xq08rB8WDcIJ3Um5o\ntqVYaHbvBc8/0uc9O3da5L1nU4QiAwOdRJOm+9z17zXeti+/PxAwprZJM2M/89sTGD8ifHpJT0EG\n/yxcX68/wJbSev703CrueXktdU2WgGtaLTZ+//Rydpdr5Q7D5eAW+hb5VyP0CF+oPm2pon1fH84E\nypr3A/Dlvm9jGv+3VQ/z0PdP9eSUepxGqxZmdNrIkxmaNphbjrqBERmx1dTdWFLD9Q9/w74qM23t\ndlosdiaMyCbXL0PWmCHh01bmZCRGTac4kAmXrcrjNe3BZnOgI3pYlUcz9hfGre6yiu02Bzv3N3od\nwDy8v7w0IKxKNOP+h5iphR5BrS31HtsN5sgDewGXy/cQcrqcUeNsrQ6rt8xgR2P7M03tmgZ0ZMFU\nzhz9w05d+9yH22htt/P+sj3MnKh51o4ZkhlQtKAtQlhNYfah7bzVk4TL3ewplvHJyjKaW63YHE5M\nRn3UvX2PoPYXxk0tgbWWLdbA36f0YHPAeTxiqIX4Ir+IEHfWlpVQ4ljtazDa2F6xv8/mY3P6HkyN\nbiEVCU88bixj40m9pYFyc0XHA2PEoxlnJnauGpPN7qTZ7Yil0+lYt7MagGnFuZx01FDvuMmjc73H\nWkEITagc6mFNPYm5LbQO8btLNQ128Ve7+HhlGXsONncY32w0eMzU2laK1eagrT0wZGqNWs03G8rd\n45yo+xoC+kUz7n+IZizEjZ2V5Sxa/zZNpr0hfU+uX8Tjp/65D2YVKIybrM1kJ0VOsF/ZWuU9rrXU\nRx3bXZ7asIgttdv57YzreGbTizRbzTw4969A93M017TVkmhIIMUYe3jOttI6Pl3t21KoaWyjqcVK\nWrKJUYMy0Ot0LLp1vtfp6Mmb5obEusozPjIlBxpD2uqb23nl8x0BbeHKJvoTrBk3uU3dU8fkMv/I\noTzyurZF9MXa/cyZUuQV+P4cDklZDjdEMxbixmPrng0riAGcCWbW7N3ZyzPSsPsJ4zWV66OOrWzx\nCeM6S32Ukd3D5rSzpVbzUn5w7ZM0WzVT/oe7P4vL/ZutZrISs2J+6D797mYeeG09G0tqvW17DjZT\n29ROflZSwD6w557JiUZv6M0xEwoBmBDB6UiABadqDnTBBTK+WBtoNZrTQdINrzB2xwx7vLNHFqUz\ndUwuty882tt+1f1f8+F32r/J686bzE9PVTh91ohurkToCUQzFuLCk0vfwZkQvZLMi9te46gRf+ql\nGfmwOX3mQbMt+hwrWv2FcUOUkd2jJcI8vtq/lKll47C2uEhLSCUnKZuMhM5ryg6XE0OM+92tFps3\nL3E4huR1HHt6/tzRTB2Ty9g+rkfcn5k3YxgThmWi1+n4ZGUZi7/aFXbcZT9Uot7HI4xf+3IX08bm\nsVrVfrsp7q2DcLHJackmZigF3Zm+0MOIZizEha3W5WHbT8g60++sb8KF/DVjhzO6CbCytdp7vKF6\nE43tzVFGd52Xti6O2Pft3tX8Y+PzPLDmCf6w9M6A+ceK0+WIGFPd1m7n2fe3UOYu7LBjf6j59LIf\njvMenzVnZIefp9frGDcsdk18oOKxMBRkR94+COfoFdDvFzr25tclrNhSCcBIdwnK3MwkTjwysIjD\nj+aN6dJ8hd6jQ81YUZQxwF3A98BQoFZV1b8GjUkCHgQOAGOBe1VV3RF8L2EAYE/gr7Nv5ZmVb5OT\nlMVFR85l3aebaDLtJYnOORPFC/8941Z7W8RxTpeTqtZqEg0JtDuslDUf4M2d73HZhItosbXEdf94\ne71msk82JtFmD4wJtdgCzz/Y/RnnFp/eqftH8wRfsr6c77ZUou5r4MFr5/DWkhIAxg7NZKdbMCvD\ns7nqzIk0tVojlkMUuk64Ig+/+fE0slI7LtLgX1Vpjep7eTTofb/3xSeN5St3DPPps0Ywd9rg7kxX\n6AVi0YxzgNdUVX1AVdVfAz9RFGVG0JgbgTJVVe8BHgaei/M8hX6Oy6m98f951u/ITUvjtpMW8Ms5\nZwHwfyf8DACrq5XffPwgS3Zuivvnr6r4nke+fzpA8HrwFEkAzYErEi22VmxOO8PTfV7Da6s28MCa\nx/nj8r/RaossyDtLXlIOAL+bcT2DU7U9wpEZWsalrdWBe+ufl32Nxd7OUxsW8afl94TsZa+pWMfn\ne78O0OKjman/t1Zz0rK0O7A7nFTWa+uaM8WXyGNIXirHTi7ilAhZoITuMX6E9mJ3+qwRnD93NOfP\nHc3kUbkMLeh4SyA/K5ljJwXuK08bkxtw7h+6lCU1hw8JOtSMVVVdHdSkB4I3vM4AbnOP36QoyjRF\nUTJUVe292BChzzBbLOj0LpKshRRmhO4ZpiUlobemYk9swA4s3vcSJ4y9P65zeHHrawAcMJd7hdrO\n+hL+tfnlgHG1bXUhKQg9ePZxC1O06jU7G3YDeOOO2+wWUkzx0RJb7G0MSi2kMLWA00adzHObX+aM\nUT/gyQ2h77FjMkeyvW6H1+GrtGkfOUk+R6nnt74KwDslH3Hr0TcyNG1QRM24pqGNOneWp9Z2O9c+\ntAS7w8XJM4Zy/FRNGB9R3PUyi0Js5GUm89wtJwKd92zW6XRcddZEtpbWeZOGnBllKyGepSCFnqNT\nDlyKopwHfKqqanCy2gLAX+VocrdFFMbZ2SkYjfHNYZuf3/2QkEOJrqzX6XTyxdaNHDVqLNmp8SkR\n11CheXOmGFOjzCnwgdDZucc6/oE1T/Do6X9hUHoB9659P8BhqyA1l6qWWpIy9TS0NWLQGxiS4dMw\nqlxaQYX8zGxuOH4hF/33moB75+SkkJ/W/b8xm8NGm72NMTnDyc9P55T8OZw4/hgSDCZe3PYaZmvg\nu25acjK7W33hKQ5TO3l5afxj9UskGQLNmuW2/UzLKwYgOTEh5HvbUhbolOaJVT1p5ggKCjK44OTe\n30oYSP9u47nWJ343nwV3fALA2JG55GYGvijefc1snn9/C6fMHk1WH9Uolt82dmIWxoqinAiciGaS\nDqaKwODIDHdbROr9SoXFg/z8dKqre8bZpj/S1fXe+b8XqNBv5ZMt07h1/qVxmcv3u7Q9R9P/t3ff\ngW1W5+LHv5qW94hnHDs7J3sQskggEKAkZRYKtJTZsgopq5ROClz4QbkNBcq40Etpob10hR1mIISR\nhIQMyCIng8RO4sQj3o5t2ZZ+f7yyhveWJT2ffyJLr6TzRLae95z3nOe47e22yeaOph5fJa6X133O\nKWMmden1O4u15TXXx9f8hRumXMXBigLvfXazjUkpEyiq+Qx9KI/fb3wSgKcWGT30Blcj961+FABz\ng5Xi4iqunvh9/urpdQIUllRgqu3el9r+inz+s+d1rphwCVmxxvKfMs8sbYcpukVcdTy84B5uXnUX\nADdOvZpntv6V2jonx5p8k6zyS45y6+77OFpT2Or93t61irExY433Lj0U8PqllXU88tJmwBiGPlzi\nS/p2E0H5+4mkv9u+jrWh0TcZsbGugeIWVbeyEh386vKZNNQ5Ka7r2SYhvSGfbfvHtqVLs6mVUmcD\nZwG3AplKqXlKqRSlVPNp9FvAPM+xU4CvZIh68DlWXc1R807jtrO4k6O77t39qwEYEp3S7jHXzfhe\nwM//2vfPPnv/lteBv6k4wKHqgoD7Fo84nTibcT3O/9pv8/XXV/a86b0vI9ZYAjIrcwbzh/q2uOvJ\nrOZlm54kr/IgD6x/hPcOrGLZxid558AHAMTb274+eOOsKzh31FlMHjIBEyaa3C7K633JeNXBT1sl\n4usmXwFASV0pd699CGi9jGuvX9GJy84cx7KbTgIgLckh1xVDkM1qITXRQXZqrAxFh4GuzKaeCfwL\n2Ah8BMQCTwHfAUqB3wGPA8uUUr8BxgA/6q8Gi577bL9vW73j5hIaXU1Ye7ml4DNr3qTGbszavGzG\nGe0eNzo1E3t9Ks4oo9ykyd2zJe5Fx0tocDWQHeebbFTXomcMcMSTrGKs0RxvrGXiEMXecmOot3l/\nX4CPD63ljNyFfHJ4nfc+/92NLhv/XSqd1Wwr2cnRmkKGxfd8Vuob3xhDivsr8wFIsLV9hrxo1EkU\nxxsnGGaTGafLyZGaQobGZnqvX7c0Na3zUYbm4g8AI7PicditPH7LAqyWjmshi8HrgWvnSCIOE12Z\nwLUJ6HCKn9a6Fri5rxol+l5dg5P3il7B+51rdVJUVcnQxO5VTKprcOJyu6hvMHqJ2+qNnZCGuieT\nHNv+r4ndauPRJXd5h2DdnRQIac99nxvDyvOyZjF/6BxGJubypWfv3impE9lWspNYWwwFnoR7y4wb\nSIyKJ8Eez1v7VwIEbKX4Qf7HfJD/sffnB+f/ptV7Ng8rv7V/JSdmzuhyW9s6SfA3NnlUp69hNpk5\nWHXYe3yKI5ntx74GjJnr20p2sjD7JMwmM98Zczav7n3L+9xfz77De9vtdlPgGZb+7xvn4bAbf/rx\nMdIjDmV22Ts6bEgFrgixctcWXyJutIPVyYa8XSRHx7Fw7JQuvcYTn77KrgZfD3KkybPCrcHBrQsv\n6eMWd2zdkS/YWLiFX8/+qXfp0sQUxbHaUkrryimpLQUgKzYdq9n4NT8lex7bSna2+5rzh85uc2OF\nG6Zexd1rH8Jm6d4mCEfauKbrb2Ri52UJLSYLDRgVxDJjMlgwdC7bj33NKdnzyIhJIyN3offYM3IX\nsq1kJ3vL93PdlCsZGuc3Oa28liaXm5kqrd3N54UQwSPJOAIUlJfybsEK8OSSqKZE6q3FrCx5FYDy\n2gs5f+rcDl+juq4uIBED7HdvAmBuykLiHI62ntahxqYmrJaen9m73W4e2/KM9+dkRyJpMakU1Bzl\nQGU+DovDm4gBJg5ROCwOnC6jdz88Poe8Kt/GCItyTmnzfVIcyYxLGs3u8n3UNtYRbW0d61fFO8iv\nPMg5o87yDvk2DymfO2oxdrOVl/eu4KQsY9b0jPSpXYrRf61wsiORoXGZPLTgbmKtbW9VePsJP6bJ\n1br61q4849r4iMzImd0qRCiRcpgR4In1L4HNt99psi0t4PFNRzsvwrG76HC7j502elqX23L75Nux\nOI3e5+b8fV1+XltSopMDJkFNGjKe5ChjnbPT1dDmmuD0mCG4PPsbD4sfypIRp3sfS4se0ur4ZlFW\nYzj3f776C1uKWv9//WnbC7ybt4qqBt+M8SPVRs9YJY9hUe4p/Hr2HVyqLuDiceczJmlkl2L0Xys8\nPsUoUZlgj2+31CXgfczlcvPap9+w51A5K9Ya14vH58pGDkIMRpKMI8BxV+DE9uaiFs2qm1rXJm7p\nm2NH2rzf7IxjWErXi0SMSc/izOwzAXhh/3M4G1vv8dpVRcdLvGtyH15wD2aTOaB6Vmwb2wdmepYX\nAWTHZXHW8EXcPO1HPLrwgQ4TXHacMXFrX8V+ntv+t3aPK/PbXOJA5UHMJrN3SdPQuMyAnnpXNLcp\nOSoJWzee63a7Wb56H2+sOcBDf9/Msco6ZoxNZXS2bOQgxGAkyTjMldXU0BhlJIg45zBumXQrQ2IC\nayw7Te1PpnK5XFTX1XGo0hhyHW2ZxZUjr4VGY8zb6u7+8PTZk2Z5bx84Ziyx2l9SyC/eexJd2H4P\n3O1uvdFEWb0RW/PQ8Sy/CVaWNpJXc68YjGvINouNiUMUdkvHE5nmZJ4Q8HOtX41r/4lazcuJjjcc\nJ6/qIMPjh+Gw9rzgwgnpU7GYLCwcdlK3nqfzy3l3Q37AfWNkRyUhBi1JxmHuiXW+3YEeXnwLKiOb\njPjAoUq3vYb9JW1PNnrk439x12f3sqduK243fG/6GcwZOQ6sRo82y5HT7TaZzWZSG43CFKv2GkUo\nlm3+I1W2fP644/F229KcSMcljWZc8hjv/YtyTvb2IM0mM+eMPAuAsUmtZytfMNq34UJ3lvP4l5+E\nwN2dmmc7A3xTfgCA9/NW43K7urTkqCMXjjmHh0++hzOHn9qt5xW2UVQnO7VvKq4JIfqeTOAKd57e\npKPeNzybFte6h/TilhXcc6axPHzF9vUcrCgiryqPKns+JjNgrsNen9xqKZQa0rVrny053UZFoG31\nnwDneJM7wNoDOxiZmtHqOW7PFoxmkzngenDLRLV4xCImp04gK7b1/q3JjiR+MevWbu8R3HJ4uaS2\n1FsD+7Etz3rvfzdvFeeOXszXpbuxmW2cNmxBt96nJZPJ1OaEsc6UVxv/v2ecOIyNu4o4f8FIpo6W\nmtNCDFaSjMNctDUa3HDO6DO9940c0jpJRfvNzn2n6GXjRouRW3cb+xGnx/V0W8EWr9Vo8ybkirq2\ny8q5PCcWJpOJOJvRyzNhapVYTSYTOR0U58iJz273sY78Ytat/HHLnzjeWEt9U327x20q/JKjNYUM\njcvq9nKovnKs0hg6X3TCMC47Y1wnRwshgk2GqcOc02UkuBibr3dlt9qYn7Ak4Lg89xaeW/c2t73z\ncLuv1XztGSCHaZicsYzP6P4wNcD1My/23i6oKANrA+4mY6i5vqntOrrNw9Rmk5mMGOOEoq0ThP6S\nE5/NDyYY7fZv40lZswOOe37HSzS6mzo8IQA4XFLDJl2Ey+1m5RcH+fOKnW1eF++JknLjmnZKkDYI\nEEJ0j/SMw5zT5QQLxEUFDnVeNG0Baz59J+C+zcdXY2rx3W12xjMpfjrb6j/1FfmAXm8yMTI1g2hn\nJrX2ozy89hmIAltjAo2WMhpdTa2Ob3Q1sq/CKGdpNpmYnXkCr+97m/nZc3rVju6K8kz0qm/0JWMX\nrlbHXT7hEib7ldVsyeVyc/dz6wEYnZ3AvsPGjPdZE9I5Pb33OycdKT1OaqJDKjQJESIkGYe5Bm8y\nDlzmE2XzDZ8mNoygwnaAtuYzPbH4bs+tc/u8bRZPFZLGKKMgRYw5gUrKaHK3Tsav7n2L1YfWAGDG\nuGa87JT/6nA5Un+I8mxZWN9Uz+82PMbBFhtSNJuXdWKHr1N53JfMmxMxwGP/2UpmegLHSmuIdVhJ\njIsiMbb7JSsbG13ERQdniFwI0X0yTB3mGt3GMHWCo/Wa21OTzyWX6Tx41k2Mswb2MIe6J3PXtJ/1\na9uspsBzwcWjjApYbSXj5vrTACZPIYyBTsTg6xnXNdW3SsTjkkYD8J0xZ3f6Os+/9XW7jy1ftYff\n/2ML9/7lC25/4rOArfK6qtHlxiIbCAgRMqRnHMaOVpRRSyVul4n4NpLxxTNO9t7OScxi9zHj9ulD\nLuDCad1b19pbZmcsiQ5jUlaR85D3/m3fHOPD5VtxZfiGgs1B3GGouWf86eF1rR77wYTvcrSmKGDX\np/Zs32/Uzh6RGc+Bo4ET1mpqAwuh/OmNndx84RTqnI0UltYyvEVJyyaXC5cLbFbfuXVTkxuLWc61\nhQgV8tcapp7//D3u3/QQLnsViU25ndaAHp7sW0o0Irn1sqL+UGb2FaWwuKOwWYxzw8aocg6VGlst\nPvrvr9i6t4Rav2u0dY3tz2Tubx0tiRriSGFy6oQurV8ekmAk9dsumcbU0UYZzhPHG5PSvj5QGnDs\npt3FFJYe56Y/fMJ9f/2CbwoCK6o9/p+t3LBsNX97X1Pn2WC+qcmFxSI9YyFChSTjMLWp8hPv7QnJ\nqtPjU2N9k4bSEwamfrHJ4ht+bTI1UO9XGvPBzctwuV2Yk4oAFw1uXwLeWaoHpH1tsVts3pncEDgk\n3dUiIi63m/JqJ6OHJpAQY+eqxeM5ZVoWV57V9uc0eWQKX+wq8v58qNiof71JF/N1Xpm3l/3R5sNs\n0sW4XMYcc6sMUwsRMiQZhymzyzctOi2287XA/teU0+MGZmefxWkXeW+7TA1MHTbC+7PJ7OKuD/6b\nqHGbsWbvI87c0/XMfe/6KVeSHpPK0unXckbuQn446QdcM/H7bR575FgNf16xk9JKX8nMquMNNLnc\nJHmWHSXHR3H1kgnERdv49ZW+GevzJxtbIDa53Ow/4usNF5fX8szr23nq1W38/h9bAt7v468KqK4z\nTmpKKjreT1kIMXjINeMw5bL4voizEjuvvBQf7UvGduvAzMI9d8ocNrz/JaXWfYAbq9lCnDOHarux\nrWGtxejxWTPyqHY1ep83LbV3JSZ7KzM2nXvm3uX9eWZG+7tW3f/CRuqcTazZfpTFc3LR+eXkpBvX\nxpPbWAM8emgi3100lryCCq44S7Fm+1GamlxU1PhGEd5al9fqed89dTTLV+9j76EKbvvjZ4AkYyFC\niSTjMPT61s/B0oitPoXzR3+b6X49zvZYzRYuG34NtgGeoTwjYwofHtvHWIeR0O5ddAN3fvabgGNM\nVl8ifnD+3cTbQ6fGcp3Tl0TfXW9cI2/u5abEt13m8qqzJ1JcbEzqsphN1NQ1crT0OLkZceQXVrf5\nnMWzc1m+OnBLSv8JXUKIwU2ScRj6oGAl2OH80Wdz2rgpXX7e/NET+rFVbbtgylzGFAxl8lCjznO0\n3Q71MRDVeqODhoPjqKow4UhyE9X9pbcDrqyq44lmJ4zrfMTCYjFxuMTYCWrKqCGMzU7iw83GbPNH\nl85n96EKZo5Lw2w28ZMLp/DEK8Zey3abmQevm9vLCIQQA0WScZhZvuVTXHajVzUrd2yQW9M5s9kc\ncK0Y8CbiprI0LMnG7khNlSk0HhnFb5/fwNhhifzy8pkEU0Ojq9Oe54Ejle0+lpESQ3pyTLuPNzOW\nJxnLurKGxDBTpVNx3MmiGdkkxkUxa7xvMtmMcWn8+ILJrNp0iGu+PZ6UhO5vMCGECA5JxmFkY94e\nPip7EwCTM5Y4R2h+GTdXBMusm0UxbwMQXZtN8+KmPYcqgtc44Ou8Mn7/jy2cPW845y8YyTuf5+EG\nzpsfuIPV/qNGMr7j0mmMG5bESx/s4VuzcrDbzCTEdK1r71+4Y9ywJKJsFm66YHK7x88anx6QoIUQ\noUGScRjZU+LbV/eS0d8NYkt65zen/ZDiqipyT0tl6UdGMq6ubezkWQOneQbzW+vyOFhUzdZ9RrWU\nlsl498EKTMCIzATsNgtXL+m8GEhLUTYz1bWQGGcnNal14RYhRHiQGR5hZOex3d7bJ43q/hf/YBFj\ndzB8SBomk4kUh7Hm2WH2DenOHJcWrKZRUxdYHas5EYOx+UOzovJa9hwqZ3R2Yq9qRJ84Ph2L2cSi\nE4b1+DWEEINfpz1jpVQm8AAwTWs9q43HTwUeA5r313tLa/37vmyk6JpSjCUvl+Rc0WnFrVBx24wb\n2Fe7l5d21gNGIgxiNUyqjhttGJYWy6HimoDH1mw/widfFZCVEstn244AsHB6x9soduaS08ZwwYJR\nRNnD4/MUQrStK8PUC4DXgekdHHOb1np1n7RI9EijqwmsDZid8Swc2/UZ1IPdkOgUxueeztuxH1JZ\nbSTCJtfA7WHcUm29MVw+cURKq2T8l7d3AYG7MJ3kKdzRUyaTSRKxEBGg02SstV7u6f125Aql1IlA\nAvC/WuuDnb1ucnIMVmvffsmkpQ1M5ajBwj/eY1VGAogxJ4bl/8OvrpnDn9/Yzhc7C7HZrCQlx/Dw\nixuZOSGDJfNGDFg7CsqNQhqpyTH8z88XsWHHUTbrIr7aU9Lm8ek93Js4HD/D9kis4SuS4u1trH0x\ngWsncL/W+oBSahKwUik1UWvdesd1P2VlrdeR9kZaWry3UEIkaBnvvuJCAKxuW9j9P6SlxWPHzQ8X\nj+eLnYXU1jXw2qo9rN9xlPU7jnLimCED1pYjhcb/rauxiSgTnDw5kz15Za2Os1rM/PLyE3r0WUTS\n77LEGr4iKd7uxNpe0u51MtZaF/nd3qGUSgJygNY1+0S/ySs1knG8rWc9sVDQvCOgy+0mv6jtSlT9\naZMu5qlXjaIajijfn07z9eFm154zgbkTMzHLRg1CiC7q0WxqpVSsUirNc/sXSqkUz+0UwA4U9l0T\nRVccKDMSQnpM51WdQlVzcnO53JT7VbdquaXg4eJqnnh5K7sPltOSy+3m/hc28unWgm6/f3MiBoj3\nmyE9YXjgLlcnTc6SRCyE6JZOk7FSaiFwBZCllPqNUioauBq433PIAeBxpdQvgceBK7TWUqF+AFXX\n1bHp+CoAZueE7pKmzpg906i/zivjy72+a7QPvLgRl9uY1OVyu3nw75vYsqeEFesOtHqNlV8cZP+R\nSu9kq64qrw4sbZmTEee9/aOzfWVErz9vYrdeVwghoGsTuD4GPm5x91N+j/8T+Gcft0t0w/MbjMIY\nJmcMk7OHB7k1/aej/YLLq+pJSXCwWRdTW29szlBZ42x1nM739ZY/2nyIE8en8+qn+zl5ahYjs9of\n4v9w06GAn4f4lZr0330pPanzEpdCCNGSFP0IcYWVFejGzwE4f8QFQW7NwEqKs5MUZ5SVvPPptVQe\nd7J9v68IR1vJKSBmvwAAE6JJREFUuNBv4uDB4hoeX76V1VsOc/8LGzle136Vr6KyWgAmj0zhxvMn\nBZwY+N/OSJEqWUKI7pNkHOL+snEFAG43nDm+o6Xg4ae82slpfpWpvtxTwmHP2t/hGfFU1jQEVMU6\nWnqcI8d8yXj1lsMB15s/3NT2irzK406+2FVErMPKrRdPZfaEjFbH/L/r5nDHpdOIdQzMXtBCiPAi\nyTjEJdqNafLToxcGuSUDKzstlpsumMw584aTlmQMGX/8ZQH7CiqxWswMS4vF5XazZU8xq7ccxuVy\ns2LtgQ5f89VP97c56euFd4zry6mJ0Z5dlFrLGhLL5JEDt8RKCBFeJBmHsOq6Og7VGJtDDE0I31nU\n/h66fi73XjOL+380hxPHp2MymVh64VQA9nu2LGxscqFyjRnOT726nRff06zfWciwNGPS1Q/OHOd9\nve+cPJLHb1ng/fl3/7eZI8d8lbU26WK2eAp6nLdgRL/GJoSIXJKMQ1RFTQ1PrF1OuW0/AFZzZGzA\nlZESQ25G4KL55uvGzXLT4xg/PCngvv9dsZMyz3Ko4Zm+5y+ZO5z4GDsPXj/Xe9/2b0oB+GjL4YDl\nTBld2H9YCCF6IjK+wQepspoafrP+PgDumvYzhg/p2m5Ey7d8xkdlbwTcV1E38EUwBov4FnsDX3fe\nJFIToxmeEU9eoa8qzidbCzBhbPLwqytmYjGbsFqM89HMlBhuPH8Sz7y+g2OVdaxYe4BXPvkm4HXt\nNjl3FUL0D/l2GWDrvtnFoXKj57W7yLf/8MaDusuv8VXxjlb3zR0e2etbmzdkeOK2k8lOjQXgp9+b\nzsWnjvYeU+9sInNIDA67lTHZia2WMqkcozedX1jVKhEDOOxy7iqE6B/y7TKAdhcW8PcDz2PVSTy+\n5FdU+vVmLaaunRdV19VR6j4MTRZun3YLOcmp2CwWzO1MLIoUP/z2BK48S2G3+TYfiYu2sWTucKqO\nN/Duhnyg46HmhFg7cdE2dvmtRT5v/gjOODGH8ur6Xu1LLIQQHZFk3Ide27qO2bmKoUkpbT6+If9r\nABqjysk7VkxprW8IdeWx13h/5ZuYLE1Mss/npgXnt3r+J3t38K/8F8AGw63TGJOe1T+BhCCz2YTd\n3PYuYPGxviTqX6CjJZPJxLicJDbvLgbgggUjOW/BSABJxEKIfhXZ3ak+9O7OTawseZUH1z+Os7Gh\nzWPyK33D0k9/8Q/yKgLrI5ssRuWoHc41bT7/5T2+68Q/Wfjd3jY5YvgPL/tP3mrL6KG+oetR2eG7\n6YYQYnCRZNxH1hzaBIDbVst9Hz7X5jElTu8GV1SbijlWX9zp627K38cd7yzj2bUraIwytuq7YdxN\n5KZGxlKmvuCw+3rMJ4zreJLc3EmZ3tsjMiUZCyEGhiTjPlLqt2Nk83IjgGfWvMnSd+9lX/FR6i1l\nmJ1xxDlzwFZPDYH74I61zPbe/sfGjyioKOP5vc9SH1XE1rpPABjGFKYOG9G/wYSZaM92hzarudPh\n5uT4KMZkJ6JykmRoWggxYOSacR/YXVgA1sCh6WfWrMBsMrGt/lOwwx+2/QGsEN+QTbwtgWoO4rbX\nQEMUd85cSoIjliFxcdz6zh4ao8r4rPIdGne7Wr1XRkzXlj8Jn0kjUjhj5jBmqq793/3y8hNwuzs/\nTggh+ook4z5wqNwYbh7GFIrqj+CMKmFb/SdtHpsVk4XVbOWQZ0c+qyuakam+Wse50aP4xmUMeW84\ntgbskMM0DvIVAGmxya1eU3TMZjVzmV/Vrc6YTCY62CBKCCH6nAxT94H88kIA0qKHEGXquErTEjWX\nhaN8Gzo02ANrIV8/9zzvbZfdWPq0cMRMHM4MhptmcPakWX3VbCGEEIOE9Iz7gC7fDTaYmzuJij1V\nVLnyAw9oiGJc9HSumfVtEqI9W+wZq5xwOAOHTuMd0Vyae5WxhMljRs4o5o36aX+GIIQQIojCvmdc\nWFnBHe8s472vN3Osuppth/M6f1I37C8ppMJyCJMzholZOaTHtt6557/m/5xbT7nIl4iB3510H6PM\nM7lz3o9aHb9g1ATv7cSGEThs9lbHCCGECB9h3TPenL+PP+99FqLgjYOv8FF+JlW2fOYWfIsrZp3R\n69cvKC9l2dZHMJkhlhTMZjOZ8alQFXhcYnTrDefjHdH89NRL23xds9nMnVN/yjMb/80lk7/d63YK\nIYQY3MIqGTe6mqhzNhDnMPa3fXHHcvAUXHKbG6kyG8PHn1e9z76VeVhMFmxmG3eccgl2q413d27i\nzYOvYXbbOH/EeWQlpDBpaG6777fuwE7v7ViLsT1fVnyLCVYNUVgtbVeG6sjI1AweXvyTbj9PCCFE\n6AmrZPz4J8vZ1/AVN064noPlxTREHQPA7QaTOXCZULHFtzHDU2vs3L7wYt7Kfxvs9bio59WCl6AA\nbmIpTS4Xz+5+mmz3ZH51+pXe5607ugHsEFWfxu2nfR+AiVk5jNg9g0npYxiXNoy0eCkcIYQQomNh\nk4y/ytvPN65NmCzw7O6nvfdnu6dQ01jtLcSRy3Ty+TLguXvrv6K4+iyarDW0XNHy9PZniWpKhig4\nbNpOdV0dcQ4Hm/L3UWs/iqM+g0eW+CZXmc1mfuZJzEIIIURXhM0Erj+te63N+68+8RzGJhnb6Fmc\nCfx80WWYnXHex6Pq08Dq5N4ND2Ayu0hsGMETp/6Oa8feaBxgbaA+ylfG8pWtnwHw+q5VAKjE8f0R\njhBCiAjSac9YKZUJPABM01q3WuSqlDIDDwLVwHDgz1rrz/u6oR3ZX1JIkXsPloZ4zG4LjVHG2t2F\nSecwNDGZy2edjmWThW+pEwHf+l2A+05byi/W3uP9OcmejNlsZlr2CNjT+r3WV7/P+vc/8lbcGpua\n03+BCSGEiAhd6RkvAF6HViO4zS4BErTWDwA/B15USnV/xlIv7C0+jMnsZn7aKVgwlgFluCZwyQmn\nAGA1W7hi1ulkJCQCEFWfDsC3Ui8k3hHN4rSLvK81Z9hkwBhuvnbsjSjrXBIahvPL6Xf53tCv9OVp\n46b2a2xCCCHCX6c9Y631cqXUqR0ccjbwvufYUqVUHTAJ2NonLeyCMyecwBw1jgRzHNOPjualre9w\n80kXtXv8H5bcSWNTk3eW87lT5uDYFcXRqhIWjp3iPW5Gzihm5Izy/jw77kw2VK/0/nzN6Ov6IRoh\nhBCRpi8mcKUTuLK20nNfh5KTY7Ba+64DnYaxT21a2gROnjKhk6Nbuyzt5E6PufPsC3lspZm1pe8B\nsOTEE7r9Pn0pLa3jvXnDSSTFCpEVr8QaviIp3t7G2hfJuAjwb0WC574OlZUd74O39klLi6e4uKrz\nA3vpokkns/XDnYxNGjMg79eegYp3MIikWCGy4pVYw1ckxdudWNtL2j1KxkqpWCBGa10MvAWcAvxN\nKZUCOIAdPXndUOCw2aUYhxBCiD7VldnUC4ErgCyl1G+AR4CrgSnAjcC/gRlKqXuAXOBKrXVTv7VY\nCCGECDNdmcD1MfBxi7uf8nvchTGLWgghhBA9EDZFP4QQQohQJclYCCGECDJJxkIIIUSQSTIWQggh\ngkySsRBCCBFkkoyFEEKIIJNkLIQQQgSZye12B7sNQgghRESTnrEQQggRZJKMhRBCiCCTZCyEEEIE\nmSRjIYQQIsgkGQshhBBBJslYCCGECDJJxkIIIUSQSTIWQgjRK0opySW9JP+Bg5RSamiw2zCQlFIj\nlVJxSilTsNvS35RSo/xuh3W8SqmJSqmRwW7HQFGGC5VStmC3pb8ppaYqpZYrpRK01q5gt6e/eb6j\nYvvrb9baHy/a15RSDuBxYI3W+kWllDlcP3ylVAxwDnCxUmoP8IHWelWQm9VvlFJxwGLg+0AhsBF4\nPqiN6kdKqSXA80qpu7XWz2GcEDcFuVl9TimVBPwamA8sBfYrpUxa67As+aeUigaWAAuAdUAiUBLU\nRvUTz2f7C2Ay4AZmAx8EtVH9yPMddQ7wHaAM2EA/fEeFSs84B4gHHlNKWcI4EU8GngIOAbcCMcCM\ncB0CUkqNAP4AHAeuA/KBYZ7HwqrH6PcZuoBVwFVKqUStdVO4fb5KqbHAS8Au4GQgTyllByyex8Pq\ns/WYDTRore8AtgGNnk5EWMWrlJoPrAeOApcCLwPfeB4Lmzibef42l2KcXF0P7ARS+iPWQf0l4Pcl\nlaa1vgzYg/HlHa7XKA4AVcAGrXUBxpdZbriefGD8QZdrrd/WWpcCcUC1UmpIOPWgPD3C5s9wDPAK\nxhf2nUqpFIyTrnByENiE0UO8BvgJ8ChwJ0CYfbZmzxfzqUCDUupC4BLgHowT67CKF/gSeEZr/ZjW\nugbIAi6AsIuzmQVj5O6g1roCsANpwNS+fqNBl9A84/LXt7gOsd3z7w+BpUqpUVprV6ififnHCqC1\nrgZ+q7Vu9ByyF/jEc2xGkJrZZ9qItw54yPPYNCAZiAJeU0pd5Lk/JD/jFr/HbqWUxfNQCfA+8Blw\nBXCX53MPi1jB+7muwvh7/VhrfS/wFvAtpdSpQWtoH2n5HeVJQgUYl9IKtNb/BTwNzFZKfSeoje2l\nNj7bGozYmn2E0YkI2d9ff23E2wC8DnxPKfUqkIBxsvlPpdRlnuf0SdyDKhl7hrLuAi4Ezm++X2td\n6Rme3oEx/PWo56HUgW9l3+gg1nK/w2YDH3iG/ZYObAv7Vgfxlnlufq21vllr/RCwAhjqeTzkzrbb\nilVr3Xxd+AzgcmAkRsIaoZSa4jkmLGIF0Fp/BPxJa73Hc9dqYAvQ2PI1Qkl78QJ/BVKAeQCeuP+P\nQfYd2x0dfLb1foeNAWZ47g+5319/HcT7KPArjO+o32qtnwT+B6OH3GdxD7ZfFDuwFWMywLzmWZie\nM4/mgK8CzlVKvQSEcm+xo1ibh+FzMH4pngYqQ3xovr14m2PK8fw8H5gJfB6MRvaR9mKNwkhIh4GH\nPY+fBiwK4c+2zVgBtNa7PfMgAKYAuRg9yFDWZryeHtTPgDuUUlme3+OJGNcYQ1WH31EebwCxnklO\noa7d32VgGnA7gFJqAUZHaW1fvnlQ9zNWSo3HOAv5ANipta72DOdNA37sue9Rv+MdGGdhlwNPaq2/\nDkKze6Q7sXp+2edjDO39FXhWax1Sf9Q9+GzvAqYDK4GVWutDQWh2j3Tzs43XWld5Zt+ejnG2vS9Y\nbe+uHnyu9wOjMC63vBVKnyv0KN7bMeY+NAEvaK0PB6HZPdLdWD3PmQMMB172G/0JCT34bP+JMdl0\nD/BiX3+2A56Mm5c3KKV+jDH+vh9YCMRqra/2O+4WjKnzjzYnXU/vIab5Gttg18tYxwNTtNb/GfiW\n90wv480ARmit1w98y7uvN7H6P3+Am90jvfxc04AcrfXmgW95z/TBZ2sJlcTU21hDTS9/lx1Agta6\nqD/aNqBDY54eX7TnxyTgXa31v4HfAhcppb7ld/h/ACfwiFLqZqWU3TNZImQSMT2P1aG13hVqiZie\nxxultS4MpURM92Nd1vx7DKFzfa0PPtfiUEvE9OI7CgLmBwxqfRFrKOmD3+W6/krEMIDJWCk1D2NZ\n0jKl1CSMs5HhAFrrYxhLAZb5PcWCcU14C8aQgHOg2tpbfRBr3cC2uHf6IN56QkQvYv2SyPs9DpnP\nFeQ7ijCNFULjd7nfh6k9F/bvxRhn/zfwHEaA5cBSrfV4z3FRwKvAz7XW25RSqYAjlK4xRVKsEFnx\nSqzhGStEVryRFCuEVrwD0TN2Y8we/UAby1juA2Z7poc3KqVu8xw3BKPIxU4ArXVJqH3wRFasEFnx\nSqzhGStEVryRFCuEULwDUZv6OLBca33Q7751nn/vBhYrpX4PVAKbQuV6SzsiKVaIrHglVkO4xQqR\nFW8kxQohFG+/J2PPRBX//4jhQPNsPDvwIMbi6f2esfuQFUmxQmTFK7GGZ6wQWfFGUqwQWvEGY9em\nLKBUKfUPoB54X2udF4R2DIRIihUiK16JNXxFUryRFCsM4ngHdJ2xUioTo2rJNuDfWuv/G7A3H2CR\nFCtEVrwSa/iKpHgjKVYY/PEOdM/YBfwZWBZqyx56IJJihciKV2INX5EUbyTFCoM83qCWwxRCCCHE\n4NsoQgghhIg4koyFEEKIIJNkLIQQQgSZJGMhhBAiyCQZCyGEEEEWjKIfQog+pJSaDzwATMQodp+M\nscH9X7TWyzt57tXAqdpvL1chxMCTnrEQIU5rvQZ4AaOk341a60uBa4G7lVK3B7d1QoiukJ6xEGFI\na31EKXUX8LJS6hXgKWAHxu40G7XWzyilxgKXA9lKqSeBN7XW7ymlbgHGAbUYm7DfrrWuDk4kQkQG\nScZChK8vgFggHXhEa/0RgFJqq1LqDa31HqXU3zGGqZd6HjsdOE9rfYbn5weAu4DfBiUCISKEJGMh\nwp8ZOFUp9X2MLeVSgNFAQRvHLgFSlVLPeH5OBY4MSCuFiGCSjIUIX7OAGmARMENrfR6AUmo6YGnn\nOSZgndb6x55jTUDMALRViIgmE7iECEOeHWr+G7gH4zpxqed+MzDM79A6wKKUMimlrgLeAU5TSjWf\nqF8A3DZgDRciQslGEUKEOKXUPOB+YDKwHGNpUyLwN631v5RSucA/gT3AMeB8YCvwIyAaeBnYC6zS\nWj+vlLoNOAljU3YH8FOtdd3ARiVEZJFkLIQQQgSZDFMLIYQQQSbJWAghhAgyScZCCCFEkEkyFkII\nIYJMkrEQQggRZJKMhRBCiCCTZCyEEEIE2f8HwcGnJoWwFP8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "AAPL[['Market', 'Strategy']].cumsum().apply(np.exp).plot(grid=True,\n",
    "                                                    figsize=(8, 5));\n",
    "# tag: AAPL_wealth\n",
    "# title: The Apple stock performance vs. investor's wealth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Listed Volatility and Variance Derivatives** |\n",
    "<a href=\"http://lvvd.tpq.io\" target=\"_blank\">Listed VV Derivatives @ Wiley Finance</a>\n",
    "\n",
    "**Python Training** |\n",
    "<a href=\"http://training.tpq.io\" target=\"_blank\">Python for Finance University Certificate</a>"
   ]
  }
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